The shaded region in the figure is the solution set of the inequations

  1. 4x + 5y ≥ 20, 3x + 10y ≤ 30, x ≤ 6, x, y ≥ 0
  2. 4x + 5y ≥ 20, 3x + 10y ≤ 30, x ≥ 6, x, y ≥ 0
  3. 4x + 5y ≤ 20, 3x + 10y ≤ 30, x ≤ 6, x, y ≥ 0
  4. 4x + 5y ≤ 20, 3x + 10y ≤ 30, x ≥ 6, x, y ≥ 0

Answer (Detailed Solution Below)

Option 1 : 4x + 5y ≥ 20, 3x + 10y ≤ 30, x ≤ 6, x, y ≥ 0
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Detailed Solution

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Concept:

 

The intercept form of the line is given by: 

Where a is the x-intercept and b is the y-intercept

 

Important Points:

  • Make it a solid line for  ≤ or ≥, and a dashed line for  < or  >
  • If the equation is given in form of  > or  ≥ then shaded area must be above the line (Away from the origin).
  • If the equation is given in form of  < or ≤ then shaded area must be below the line (Toward origin).

 

Calculation:

 

Equation of line AB: 

Equation of line CD: 

Equation of line EF: x = 6

Here we can see the shaded area above the line AB, Below the line CD and Left of line EF

∴ 4x + 5y ≥ 20 ,  3x + 10y ≤ 30, x ≤ 6, x, y ≥ 0

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